Question

log(3)(a1)+log(3)(a2)+.log(3)(a10)=10成立的充分条件是

Answer 1

1）在等比数列{an}中,a5*a6＝9 题中好像少了(an>0)

则由等比数列的性质 ai*aj=ak*al (i+j=k+l)

a1*a10=a2*a9=a3*a8=a4*a7=a5*a6=9

即

a1*a2*a3*a4*a5*a6*a7*a8*a9*a10=3^10

对上式两边取对数

log(3)(a1*a2*a3*a4*a5*a6*a7*a8*a9*a10)=10

即

log(3)(a1)+log(3)(a2)+.log(3)(a10)=10

2）同理可得